Probability convergence with OLS estimators - univariate vs bivariate

where (1, , ) is not perfectly collinear, < and < (** - please note it should be in the above, not just , but my Latex-fu is weak).

Suppose a professor estimates the equation: = * + * + *

by OLS. Show that:

* p + Cov[ , ]/Var[ ].

Also, under what conditions will it be true that * is consistent for ? (Here I'm confused - it's obvious that (X'X)^-1 is well defined since they already explicitly stated that (1, , ) is not perfectly collinear and that < and < ).